Optimization-based design of plant-friendly multisine signals using geometric discrepancy criteria

System identification is an important means for obtaining dynamical models for process control applications; experimental testing represents the most time-consuming step in this task. The design of constrained, “plant-friendly” multisine input signals that optimize a geometric discrepancy criterion arising from Weyl’s Theorem is examined in this paper. Such signals are meaningful for data-centric estimation methods, where uniform coverage of the output state-space is critical. The usefulness of this problem formulation is demonstrated by applying it to a linear problem example and to the nonlinear, highly interactive distillation column model developed by Weischedel and McAvoy. The optimization problem includes a search for both the Fourier coefficients and phases in the multisine signal, resulting in an uniformly distributed output signal displaying a desirable balance between high and low gain directions. The solution involves very little user intervention (which enhances its practical usefulness) and has great benefits compared to multisine signals that minimize crest factor. The constrained nonlinear optimization problems that are solved represent challenges even for high-performance optimization software.     

Robust suboptimal control of nonlinear systems

In this paper, we consider a nonlinear dynamic system with uncertain parameters. Our goal is to choose a control function for this system that balances two competing objectives: (i) the system should operate efficiently; and (ii) the system’s performance should be robust with respect to changes in the uncertain parameters. With this in mind, we introduce an optimal control problem with a cost function penalizing both the system cost (a function of the final state reached by the system) and the system sensitivity (the derivative of the system cost with respect to the uncertain parameters). We then show that the system sensitivity can be computed by solving an auxiliary initial value problem. This result allows one to convert the optimal control problem into a standard Mayer problem, which can be solved directly using conventional techniques. We illustrate this approach by solving two example problems using the software MISER3.     

Modelling and system identification of an experimental apparatus for anomaly detection in mechanical systems

This paper presents design, modelling and system identification of a laboratory test apparatus that has been constructed to experimentally validate the concepts of anomaly detection in complex mechanical systems. The test apparatus is designed to be complex in itself due to partially correlated interactions amongst its individual components and functional modules. The experiments are conducted on the test apparatus to represent operations of mechanical systems where both dynamic performance and structural durability are critical.     

Iterative identification algorithm for Wiener nonlinear systems using the Newton method

The Wiener system is an important class of output nonlinear systems. This paper presents a Newton iterative parameter estimation algorithm for Wiener nonlinear systems. The simulation results show that the proposed algorithm is effective. The proposed algorithm can be combined with other iterative methods to identify other linear or nonlinear systems with colored noises.     

Iterative learning control design of nonlinear multiple time-delay systems

Most available results on iterative learning control address trajectory tracking problem for systems without multiple time-delay. This paper is concerned with iterative learning control design for nonlinear systems with multiple delays, in which external disturbances and output measurement noises are involved. We obtain some new and interesting criteria to guarantee the convergence of the tracking error in the sense of the λ − norm. It will be shown that the convergence of the system outputs to the desired trajectory is ensured in the absence of disturbances and output measurement noises. In the presence of disturbance and measurement noises, we estimate the upper bound of the tracking error. In order to confirm the validity of the present results, numerical simulation is also presented.     

Robust control design for a class of mismatched uncertain nonlinear systems

We consider the robust control design problem for a class of nonlinear uncertain systems. The uncertainty in the system may be due to parameter variations and/or nonlinearity. It may be possibly fast, time-varying. The system does not satisfy the so-called matching condition. Under a state transformation, which is based on the possible bound of the uncertainty, a robust control scheme can be designed. The control renders the original uncertain system practically stable. Furthermore, the uniform ultimate boundedness ball and uniform stability ball of the original system can be made arbitrarily small by suitable choice of design parameters.     

Iterative parameter identification methods for nonlinear functions

This paper considers identification problems of nonlinear functions fitting or nonlinear systems modelling. A gradient based iterative algorithm and a Newton iterative algorithm are presented to determine the parameters of a nonlinear system by using the negative gradient search method and Newton method. Furthermore, two model transformation based iterative methods are proposed in order to enhance computational efficiencies. By means of the model transformation, a simpler nonlinear model is achieved to simplify the computation. Finally, the proposed approaches are analyzed using a numerical example.     

A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification

In this paper, we present two control schemes for the unknown sampled-data nonlinear singular system. One is an observer-based digital redesign tracker with the state-feedback gain and the feed-forward gain based on off-line observer/Kalman filter identification (OKID) method. The presented control scheme is able to make the unknown sampled-data nonlinear singular system to well track the desired reference signal. The other is an active fault tolerance state-space self-tuner using the OKID method and modified autoregressive moving average with exogenous inputs (ARMAX) model-based system identification for unknown sampled-data nonlinear singular system with input faults. First, one can apply the off-line OKID method to determine the appropriate (low-) order of the unknown system order and good initial parameters of the modified ARMAX model to improve the convergent speed of recursive extended-least-squares (RELS) method. Then, based on modified ARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown sampled-data nonlinear singular system with immeasurable system state. Moreover, in order to overcome the interference of input fault, one can use a fault-tolerant control scheme for unknown sampled-data nonlinear singular system by modifying the conventional self-tuner control (STC). The presented method can effectively cope with partially abrupt and/or gradual system input faults. Finally, some illustrative examples including a real circuit system are given to demonstrate the effectiveness of the presented design methodologies.     

Nonlinear system identification and control using a real-coded genetic algorithm

A real-coded genetic algorithm (GA) applied to the system identification and control for a class of nonlinear systems is proposed in this paper. It is well known that GA is a globally optimal method motivated from natural evolutionary concepts. For solving a given optimization problem, there are two different kinds of GA operations: binary coding and real coding. In general, a real-coded GA is more suitable and convenient to deal with most practical engineering applications. In this paper, in the beginning we attempt to utilize a real-coded GA to identify the unknown system which its structure is assumed to be known previously. Next, according to the estimated system model an optimal off-line PID controller is optimally solved by also using the real-coded GA. Two simulated examples are finally given to demonstrate the effectiveness of the proposed method.     

On robust identification in the square and king grids

Fault diagnosis of multiprocessor systems gives the motivation for robust identifying codes. We provide robust identifying codes for the square and king grids. Often we are able to find optimal such codes.     

Iterative sliding mode control

Iterative Learning Control (ILC) methods are described and applied ever-increasingly as powerful tools to control dynamics nowadays.

ILC’s methods in most studies are described as based on repetitive process from the beginning to the end of process or as a kind of repetitive control.

Our newly designed controllers based on a particular case of iterative learning control radically differ from conventional methods in attempting to stabilize a class of non linear systems.

In this paper two kinds of ILC method are introduced in two separate sections. In the first, our newly designed method satisfies the condition of a Lyapunov stability theorem in a class of non linear systems in which their structures have the Lipschitz property. In the second, by freezing the time and moving to a new virtual axis, called the index axis, this newly designed method tries to find the best value for control at this time step and can be used in two modes, on-line and off-line.

In both methods, by satisfying the convergence condition of our designed ILC, closed loop stability is obtained automatically.     

High performance robust linear controller synthesis for an induction motor using a multi-objective hybrid control strategy

A robust induction motor control should provide the desired performance in the face of both plant model and controller model uncertainty. In a recent work, Bottura and co-workers, using the field orientation principle, introduced a representation of a nonlinear time-varying induction motor model that admits robust induction motor controller synthesis in the linear _H∞$H_{\infty }$ framework. The present work considers the use of the approach of Bottura et al. for attaining robust performance of the main operating modes–tracking and disturbance rejection–of an induction motor control system under implementation constraints on the control signal magnitude. This approach requires two distinct mode-specific controllers with gains that cannot be bridged without considerable performance degradation. To address this problem, a multi-objective hybrid control design methodology is developed that employs the corresponding mode-specific controller in each mode, and organizes a rapid and smooth steady-state switching, or transfer, between these controllers to permit sequencing of the operating modes, as necessary. Simulation shows that the technique proposed yields controllers with performance minimally affected by an imprecise modeling of an induction motor, as well as a reduced cost controller implementation throughout the entire induction motor operating sequence.     

Efficient robust optimization for robust control with constraints

This paper proposes an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed linear constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program. While the reparameterized problem is theoretically tractable, the number of variables is quadratic in the number of stages or horizon length N and has no apparent exploitable structure, leading to computational time of per iteration of an interior-point method. We focus on the case when the disturbance set is ∞-norm bounded or the linear map of a hypercube, and the cost function involves the minimization of a quadratic cost. Here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem, that is, the policy optimization problem may be decomposed into a set of coupled finite horizon control problems. This decomposition can then be formulated as a highly structured quadratic program, solvable by primal-dual interior-point methods in which each iteration requires time. This cubic iteration time can be guaranteed using a Riccati-based block factorization technique, which is standard in discrete-time optimal control. Numerical results are presented, using a standard sparse primal-dual interior point solver, that illustrate the efficiency of this approach.     

Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems

Based on the modified state-space self-tuning control (STC) via the observer/Kalman filter identification (OKID) method, an effective low-order tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems is proposed in this paper. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). Then, the above identified model in a general coordinate form is transformed to an observer form to provide a computationally effective initialization for a low-order on-line “auto-regressive moving average process with exogenous (ARMAX) model”-based identification. Furthermore, the proposed approach uses a modified Kalman filter estimate algorithm and the current-output-based observer to repair the drawback of the system multiple failures. Thus, the fault-tolerant control (FTC) performance can be significantly improved. As a result, a low-order state-space self-tuning control (STC) is constructed. Finally, the method is applied for a three-tank system with various faults to demonstrate the effectiveness of the proposed methodology.     

Static output feedback and guaranteed cost control of a class of discrete-time nonlinear systems with partial state measurements

In this paper both the static output feedback issue and the observer-based control of a class of discrete-time nonlinear systems are considered. Thanks to a newly developed linearization lemma, it is shown that the solution of the discrete-time output feedback problem is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint. An illustrative example is provided to show the usefulness of the proposed control designs.     

Robust control of base-isolated structures under earthquake excitation

We propose the use of robust control in conjunction with base isolation in order to assure arbitrarily small motion of a seismically excited structure. The proposed method requires control force application only at the base (first) floor. The efficacy of the scheme is illustrated by extensive simulations for a prototype six-story building.This paper is based on research supported, in part, by the NSF and AFOSR.     

Volterra-type models for nonlinear systems identification

In this work, multi-input multi-output (MIMO) nonlinear process identification is dealt with. In particular, two Volterra-type models are discussed in the context of system identification. These models are: Memory Polynomial (MP) and Modified Generalized Memory Polynomial (MGMP), which can be considered as a generalization of Hammerstein and Wiener models, respectively. Both of them are appealing representations as they allow to describe larger model sets with less parametric complexity. Simulation example is given to illustrate the quality of the obtained models.     

Iterative learning consensus control with initial state learning for fractional order distributed parameter models multi-agent systems

This paper considers the consensus control problem of multi-agent systems (MAS) with distributed parameter models. Based on the framework of network topologies, a second-order PI-type iterative learning control (ILC) protocol with initial state learning is proposed by using the nearest neighbor knowledge. A discrete system for proposed ILC is established, and the consensus control problem is then converted to a stability problem for such a discrete system. Furthermore, by using generalized Gronwall inequality, a sufficient condition for the convergence of the consensus errors between any two agents is obtained. Finally, the validity of the proposed method is verified by two numerical examples.     

Modelling and system identification of active magnetic bearing systems

Active magnetic bearing (AMB) systems have recently attracted much attention in the rotating machinery industry due to their advantages over traditional bearings such as fluid film and rolling element bearings. The AMB control system must provide robust performance over a wide range of machine operating conditions and over the machine lifetime in order to make this technology commercially viable. An accurate plant model for AMB systems is essential for the aggressive design of control systems. In this paper, we propose two approaches to obtain accurate AMB plant models for the purpose of control design: physical modelling and system identification. The former derives a model based upon the underlying physical principles. The latter uses input – output data without explicitly resorting to physical principles. For each problem, a brief summary of the theoretical derivation and assumptions is given. Experimental results based on data collected from an AMB test facility at the United Technologies Research Center provide a vehicle for a comparison of the two approaches.     

Identification of multiple-input single-output Hammerstein models using Bezier curves and Bernstein polynomials

This paper considers the implementation of Bezier–Bernstein polynomials and the Levenberg–Marquart algorithm for identifying multiple-input single-output (MISO) Hammerstein models consisting of nonlinear static functions followed by a linear dynamical subsystem. The nonlinear static functions are approximated by the means of Bezier curves and Bernstein basis functions. The identification method is based on a hybrid scheme including the inverse de Casteljau algorithm, the least squares method, and the Levenberg–Marquart (LM) algorithm. Furthermore, results based on the proposed scheme are given which demonstrate substantial identification performance.